Solve (x+4+2i)(x-4+2i)

$$( x + 4 + 2 i ) ( x - 4 + 2 i )$$

Evaluate

$$\left(x+\left(-4+2i\right)\right)\left(x+\left(4+2i\right)\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+4+2i by each term of x-4+2i.

$$x^{2}-4x+2ix+4x-16+8i+2ix-8i-4$$

Combine the real and imaginary parts.

$$x^{2}-4x+2ix+4x+2ix-16-4+\left(8-8\right)i$$

Do the additions.

$$x^{2}-4x+2ix+4x+2ix-20$$

Combine -4x and 2ix to get \left(-4+2i\right)x.

$$x^{2}+\left(-4+2i\right)x+4x+2ix-20$$

Combine \left(-4+2i\right)x and 4x to get 2ix.

$$x^{2}+2ix+2ix-20$$

Combine 2ix and 2ix to get 4ix.

$$x^{2}+4ix-20$$

Expand

$$x^{2}+4ix-20$$

Solution Steps

Apply the distributive property by multiplying each term of x+4+2i by each term of x-4+2i.

$$x^{2}-4x+2ix+4x-16+8i+2ix-8i-4$$

Combine the real and imaginary parts.

$$x^{2}-4x+2ix+4x+2ix-16-4+\left(8-8\right)i$$

Do the additions.

$$x^{2}-4x+2ix+4x+2ix-20$$

Combine -4x and 2ix to get \left(-4+2i\right)x.

$$x^{2}+\left(-4+2i\right)x+4x+2ix-20$$

Combine \left(-4+2i\right)x and 4x to get 2ix.

$$x^{2}+2ix+2ix-20$$

Combine 2ix and 2ix to get 4ix.

$$x^{2}+4ix-20$$